Recurrent tensor

In mathematics, a recurrent tensor with respect to a connection ${\displaystyle \nabla }$ on a manifold M is a tensor T on M for which there is a one-form ω on M such that

${\displaystyle \nabla T=\omega \otimes T.\,}$

Example

An example for a recurrent tensor is a Weyl structure on M.

Literature

• A.G. Walker: On parallel fields of partially null vector spaces, The Quarterly Journal of Mathematics 1949, Oxford Univ. Press
• E.M. Patterson: On symmetric recurrent tensors of the second order, The Quarterly Journal of Mathematics 1950, Oxford Univ. Press
• J.-C. Wong: Recurrent Tensors on a Linearly Connected Differentiable Manifold, Transactions of the American Mathematical Society 1961,
• D.V. Alekseevky, H. Baum (2008). Recent developments in pseudo-Riemannian geometry. European Mathematical Society. ISBN 3-037-19051-5.